the two-way table below shows the intended careers among the incoming class of first-year college students, divided by gender. If a student is chosen and random, what is the probability of the student is female who intends to be a research scientist?​

After considering and calculating, the modulus of z is r = \(2^{1/32}\) and the argument of z is θ = 5π/32.

To solve this equation, we can first express −1−i in polar form as:

−1−i = √2cis(3π/4)

where cis(θ) = cos(θ) + i sin(θ) is the polar form of a complex number.

Now, we can express z in polar form as:

z = r cis(θ)

where r is the modulus of z and θ is its argument. Substituting this into the equation z¹⁶ = √2cis(3π/4), we get:

r¹⁶ cis(16θ) = √2cis(3π/4)

Taking the modulus of both sides, we get:

r¹⁶ = √2

Taking the argument of both sides, we get:

16θ = 3π/4 + 2kπ or 16θ = -3π/4 + 2kπ

where k is an integer. Solving for θ in the range 0 < θ < 2π, we find that the second smallest positive solution is:

θ = (3π/4 + 2π)/16 = 5π/32

Therefore, the value of z is:

z = r cis(θ) = \(\sqrt{2}^{1/16}\) cis(5π/32)

We can simplify this as:

z = \(2^{1/32}\)cis(5π/32)

So, the modulus of z is:

r = \(2^{1/32}\)

And the argument of z is:

θ = 5π/32

Therefore, the answer is:

z = \(2^{1/32}\)  cis(5π/32)

So, the modulus of z is r = \(2^{1/32}\) and the argument of z is θ = 5π/32.

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Answer:

undefined

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 8 - -13)/ ( 17-17)

   = ( 8 +13)/ ( 17-17)

   = 21/ 0

We can not divide by 0, so the slope is undefined

Answer:

Undefined  slope:-  the line is vertical

Step-by-step explanation:

The slope for the line joining the points (x1, y1) and (x2, y2)

= (y2-y1)/(x2-x1)  so here it is:

(8 - (-13))/ (17-17)

= 21/0

As the denominator is zero the line is vertical.

Answer:

21/60

Step-by-step explanation:

32 + 1 + 3 + 3 + 21 = 60

ans = 21/60

Answer:

Step-by-step explanation:

21/60

Answer:

ABD= 140° 180 - 40 = 140 ABD = 140.

Step-by-step explanation:

180 - 40 = 140 ABD = 140.

Answer:

independent

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given system:

The first equation is a horizontal line, the second equation is a line with a slope of -3.

Since the lines have different slopes, they intersect at one point.

As there is one intersection, the system has one solution.

The value of k in the equations is 2/3

From the question, we have the following parameters that can be used in our computation:

y = 9kx - 1

kx + 4y = 12

This can be expressed as

y = 9kx - 1

y = -kx/4 + 3

The slopes of perpendicular lines are opposite reciprocal

This means that

9k * -k/4 = -1

So, we have

k^2 = 4/9

Evaluate

k = 2/3

Hence, the value of k is 2/3

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Answer:

n=12

Step-by-step explanation:

7n-18 =5n+6

+18 to both sides

7n=5n+24

-5n from both sides

2n=24

divide by 2

n=12

Answer:

n=13

Step-by-step explanation:

7n-18=5n+6   move variables to 1 side

-5           -5    (in this case subtract 5 on both sides of the equal sign)

2n-18=  6        now you want to get the variable alone

   +18   +18     (in this case add 18 on both sides of the equal sign)

2n=26             now you want to get the variable (N) by itself

/2    /2            ( so divide 2 on both sides of the equal sign )

n=13  

Answer:

W=x/7+ 8z/7 + 4/7

Step-by-step explanation:

Answer:

164/3

Step-by-step explanation:

The spread of the data in the histogram is uneven or skewed to the right.

A histogram is a graphical representation of data used to display the distribution of values in a dataset, showing data in bins or intervals along the horizontal axis.

The data distribution in the histogram is uneven or tilted to the right. This suggests that there are fewer students who have gone water skiing less frequently (1 to 5 trips) and more students who have gone water skiing more frequently (11 to 15 trips). The frequency is greatest between 11 and 15 visits, which is reflected by the largest bar in the histogram.

In given problem, the skewed distribution of the given data shows that there are more no. of the students doing water-skiing regularly than those who are doing it less frequently.

This might imply that there is a group of students who are more experienced or enthusiastic about water skiing, and they have gone on more excursions than other students who have gone on less trips. It also implies that the majority of students fall within the 11 to 15 trip period, which might imply a common pattern or trend in the data.

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The best description of the spread of the data is that it is skewed or unevenly distributed.

A histogram is a graphical representation of data used to display the distribution of values in a dataset, showing data in bins or intervals along the horizontal axis.

Based on the given histogram, the data is not evenly distributed across the five intervals. The majority of students have been water-skiing between 11 and 15 times, with a frequency of 5. There are fewer students who have been water-skiing between 16 and 20 times, with a frequency of 4, and even fewer students who have been water-skiing between 21 and 25 times, with a frequency of 3.

The spread of the data refers to how far apart the values in the dataset are from each other. In this case, the data is not evenly spread across the different intervals. The values in the dataset are more concentrated in the interval of 11 to 15, and less concentrated in the intervals of 1 to 5 and 21 to 25. This indicates that the majority of students have been water-skiing a similar number of times, while fewer students have been water-skiing either a lot or a little.

Therefore, the best description of the spread of the data is that it is skewed or unevenly distributed.

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The complete question is:

A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.

A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 1 to 5 that stops at 1, for 6 to 10 that stops at 2, for 11 to 15 that stops at 5, for 16 to 20 that stops at 4, and for 21 to 25 that stops at 3.

Which of the following best describes the spread of the data? Explain its meaning in this situation?

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Given a ray passing through a line at an angle of 29 degrees, the angle opposite to it (angle R) can be found by subtracting 29 degrees from 180 degrees. Therefore, the value of angle R is 151 degrees.

We are given that a ray passes through a line, making an angle of 29 degrees with the line. Let us represent this situation as follows

The angle R represents the angle opposite to the angle of 29 degrees. Since the ray and the line form a straight line, their angles add up to 180 degrees. Therefore, we can write

angle R + 29 degrees = 180 degrees

To solve for angle R, we can subtract 29 degrees from both sides of the equation

angle R = 180 degrees - 29 degrees

Simplifying the expression, we get

angle R = 151 degrees

Therefore, the value of angle R is 151 degrees.

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Answer:

x= 42

Step-by-step explanation:

3x+ 54=180

straight angle is 180

So just solve the equation.

subtract 54 on both sides.

126=3x

divide that by 3, and you get 42.

check You answer by multiplying 42 And 3, Which basically Is 126

and then 126+54

which is then 180

I hope this Helps!

Answer:

(In picture with steps)

Step-by-step explanation:

^

Sorry this took so long! I was doing the work, hope it helped anyways!

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Answer:

2a. =  X = -5      2b. =  X = -4

Step-by-step explanation:

Hope this helps!

2a.   2 - 2x - 5 = 7

-2x = 7 + 5 - 2

-2x = 10

x = -5

2b.    -6 + x + 4 = -6

x = -6 - 4 + 6

x = -10 + 6

x = -4

Answer: 15-a=5

Step-by-step explanation:

15 is the amount she paid in total. 15 pounds - 5 pounds = 10 pounds

so the original price was 10 pound.

Answer:

\( \sf \: d) \: 15 - a = 5\)

Step-by-step explanation:

Given information,

→ Sophia brought some almonds.

→ She paid $15 and received $5.

Now we have to,

→ Find the required equation.

Let us assume that,

→ a = Cost of the almonds

The equation will be,

→ 15 - a = 5

=> As she is received $5 as change.

Then the cost of almonds is,

→ 15 - a = 5

→ -a = 5 - 15

→ -a = -10

→ [ a = $10 ]

Hence, the option (d) is correct.

Answer:

The answer in order from top to bottom:

22, 27, and 15

See the attached worksheet

Step-by-step explanation:

Use PEDMAS oder of operations and solve each section of the expressions using the PEDMAS rules.

The correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.

The answer to the question is option C) The speed is decreasing because the distance traveled during each time increment is increasing.

Explanation:A group of students collected distance versus time data for a model car. There could be many types of data that can be collected with respect to distance and time.

For instance, distance could be in miles or kilometers, whereas time could be in seconds, minutes, or hours.In this case, the relation between the distance and time of a model car is given, and we have to describe how the speed of the car is changing over time. If the distance traveled during each time increment is increasing, then the speed is decreasing.

Thus, the correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.

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Answer:

20

Step-by-step explanation:

2/3 of an hour is 40minutes and what’s 40/2 20

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

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x=-.7+1.8734994i  and x=-.7-1.8734994i

Step-by-step explanation:

2x+5x² +7x+10+6+4+-2x=(5x²)+(2x+7x-2x)+(10+6+4)=5x²+7x+20

quadratic equation

x=(-b±√(b²-4ac))/2a

where a=5, b=7, c=20

x=(-7±√(7²-4(5)(20)))/(2(5))

x=(-7±√((49-400))/10

x=(-7±√(-351))/10

x=(-7±18.734994i)/10

x=-.7+1.8734994i  and x=-.7-1.8734994i

A sample size of approximately 4,148 newborns is required to obtain a 99% confidence interval for the proportion of all newborns who are breast-fed exclusively in the first two months of life to within 2 percentage points.

To calculate the required sample size for a 99% confidence interval with a margin of error (precision) of 2 percentage points for the proportion of newborns breast-fed exclusively in the first two months of life,

we will use the following formula:
\(n = (Z^2 * p * (1-p)) / E^2)\)
where:
n = required sample size
Z = Z-score for the desired confidence level (in this case, 99%)
p = estimated proportion (since we don't have this value, we will use 0.5 for the most conservative estimate)
E = margin of error (2 percentage points, or 0.02 in decimal form)
For a 99% confidence interval, the Z-score is 2.576.

Now, let's plug these values into the formula:
\(n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2\)
n = (6.635776 * 0.5 * 0.5) / 0.0004
n = 1.658944 / 0.0004
n ≈ 4147.36
Since we cannot have a fraction of a person, we will round up to the nearest whole number.

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The given function is,

The graph of the g(x) will be shifted 3 units upward with respect to the parent function f(x),

Thus, the above figure is the graph of g(x).

Answer:

Step-by-step explanation:

First you add 5 to -3 so that you get 2 is less than or equal to x.

x ≥ 2

Answer:

The are of the figure is 36m.

Step-by-step explanation:

Split the figure into 2 shapes, a rectangle and a triangle

6 * 5 = 30

Rectangle = 30

2 * 6 = 12

12 / 2 = 6

Triangle = 6

30 + 6 = 36m

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-Lil G

Answer:

shov

Step-by-step explanation:

123323143423 dfghe we erewrfwefwet